Add date calculation to Libre Draw

edit

• In Calc, enter formula =TODAY() + 365 in a cell
• Select the cell and copy it
• Paste into Draw

The pasted object is a complete spreadsheet object with calculation capability. It should update whenever you reopen the file. If you leave it open, double click the date to enter Edit mode, and press function key F9 to update.

All the objects you can insert into a drawing are shapes of one or another kind, and none of them offers a service (via interface) for calculations or formatting of numeric data.
The so-called textfields you ca insert are next to useless. In specific concerning dates they aren't usable since they neither allow to define an offset (your 356 days) nor accept any reasonable format. Draw files generally don't support the NumberFormats feature.
Therefore I can only see one way:
Rely on user code (a little Basic Sub e.g.) and use the capabilities of Basic concerning calculations and formatting of numbers. The result can then be inserted into a shape as text.
Th attached example drawing is containing such a Sub whichwilol run for you as a demo. It is very primitive an will require refinements and adaptions to your needs.
C:\fakepath\ask247448shapesShowingCalculatedDate_1.odg